A long solenoid has \(800\) turns per metre of the length of the solenoid. A current of \(1.6\) A flows through it. What is the magnetic induction at the end of the solenoid on its axis?

1.	\(16 \times 10^{-4}~\text{T}\)	2.	\(8 \times 10^{-4}~\text{T}\)
3.	\(32 \times 10^{-4}~\text{T}\)	4.	\(4 \times 10^{-4}~\text{T}\)

Figure shows the cross-sectional view of the partially hollow cylindrical conductor with inner radius 'R' and outer radius '2R' carrying uniformly distributed current along it's axis. The magnetic induction at point 'P' at a distance $\frac{3R}{2}$ from the axis of the cylinder will be:

1. Zero                               

2. $\frac{5{\mu }_{0}i}{72\mathrm{\pi R}}$

3. $\frac{7{\mu }_{0}i}{18\mathrm{\pi R}}$                             

4.  $\frac{5{\mu }_{o}i}{36\mathrm{\pi R}}$

The ratio of the magnetic field at the centre of a current-carrying coil of the radius 'a' and at a distance ‘a’ from centre of the coil along the axis of the coil is:

1. $\frac{1}{\sqrt{2}}$                              2. $\sqrt{2}$ 

3. $\frac{1}{2\sqrt{2}}$                             4. $2\sqrt{2}$ 

An electron is traveling along the x-direction. It encounters a magnetic field in the y-direction. Its subsequent motion will be:

1.  Straight-line along the x-direction

2.  A circle in the xz-plane

3.  A circle in the yz-plane

4.  A circle in the xy-plane

A proton, a deuteron, and an $\alpha -$ particle having the same kinetic energy are moving in circular trajectories in a constant magnetic field. If $r_p,r_d$ and $r_{\alpha }$ denote respectively the radii of the trajectories of these particles, then:

1. $r_{\alpha }=r_p<r_d$                             

2.  $r_a>r_d>r_p$ 

3. $r_{\alpha }=r_d>r_p$                             

4.  $r_p=r_d=r_{\alpha }$ 

If induction of magnetic field at a point is B and energy density is U, then which of the following graphs is correct?

1. 

2. 

3. 
4. 

When a proton is released from rest in a room, it starts with an initial acceleration ${\mathrm{a}}_0$ towards the east. When it is projected towards the north with a speed ${\mathrm{v}}_0$, it moves with initial acceleration $3{\mathrm{a}}_0$ towards east. The electric and magnetic fields in the room are -

1.  $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\mathrm{west}, \frac{{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}\mathrm{up}$

2.  $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\mathrm{west}, \frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}\mathrm{down}$

3.  $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\mathrm{east}, \frac{2{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}\mathrm{up}$

4.  $\frac{{\mathrm{Ma}}_0}{\mathrm{e}}\mathrm{east}, \frac{3{\mathrm{Ma}}_0}{{\mathrm{ev}}_0}\mathrm{down}$

One proton beam enters a magnetic field of ${10}^{-4}T$ normally, Specific charge = ${10}^{11}C/kg.$ velocity = ${10}^{7}m/s.$ What is the radius of the circle described by it:

1. $0.1m$                               

2. $1m$

3. $10m$                               

4. None of these

A circular coil 'A'  has a radius R and the current flowing through it is I. Another circular coil ‘B’ has a radius 2R and if 2I is the current flowing through it, then the magnetic fields at the centre of the circular coil are in the ratio of (i.e. $B_A$ to $B_B$):

1. 4 : 1                             

2. 2 : 1

3. 3 : 1                             

4. 1 : 1